Vinaigrette is composed of three things oil, vinegar (in a 4 to 1 ratio) and an emulsifying agent, usually mustard. So you can experiment to your heart's content by adding asian flavors. Let's say maybe 4 parts olive oil to which you've added some sesame oil, a splash of soy sauce. 1 part white vinegar and a spoonful of chinese hot mustard. Whisk that all together until they become intimate friends.

The nice thing about salad dressing is you can just keep adding to adjust and dip veggies in to taste.
I would start with small quantities and write down what you add in case you need to double in the end.
I once threw together a tasty Southeast Asian-inspired dressing by starting with peanut butter, coconut milk and lime juice; I can't remember what else but I probably added salt, a pinch of sugar, some sriracha, maybe a couple drops of fish sauce.
Another combo I would try is 3 parts neutral vegetable oil, 1 part lemon juice and /or rice vinegar, then add some toasted sesame oil, the juice of some grated ginger, some finely minced shallot, a couple drops maple syrup (not Asian but great in salad dressings), then decide if it needs more sesame oil or more neutral oil... I wonder if you could reduce some soy sauce and add a little, or just add salt.

Agreed about the fun of improvising mentioned above. How about adding fish sauce for a Vietnamese twist? For example: 4 parts neutral oil to one part lime juice (sometimes I like a 3:1 fat to acid ratio, btw), plus some grated ginger, a little sugar to taste, and a dash of fish sauce (if you're not familiar with this product, start with very little; it's very strong stuff). You can throw in a very small amount of thinly sliced/minced chile pepper if you like heat.

I sometimes make a wasabi soy vinaigrette by mixing 3 parts oil to 1 part rice vinegar to 1 part soy sauce (preferably Japanese), add a squirt of wasabi from the tube or a 1/2 tsp wasabi powder (or you can add more if you like), couple of pinches of sugar or some honey, a small spoon of toasted sesame oil. Combine all in a small jar and shake the dickens out of it. I like a salty/sweet vinaigrette so that's why I add the sweetener and soy sauce. Put if it's too salty or too sweet, just reduce or leave out. It's all about your preference

You can also use miso for the salty element (in which case don't use fish sauce, and either skip soy sauce, or go easy on it) and ginger. I'd also use rice vinegar and a touch of sesame oil along with a neutral oil. These are the flavors in the ubiquitous Japanese restaurant dressing - which can be overly sweet and meh...but prepared freshly and with less sugar, is very tasty.

My favorite is a Japaneese Sesame seed dressing. Sorry it's not really quantified, I tend to taste and add more or less stuff. But start with this:
1-2 table spoons of sesame seeds.
Light salad oil
lemon and lime juice
garlic
1/4 of a onion
tsp of mustard
soy sauce.
sugar

Toast the seeds and grind them to a paste in a mortar. Start with 3 parts lemon and lime juice 1 part oil.
Add the juice to a blender with the garlic clove, onion, mustard and blend. Add a table spoon of the sesame seed past and blend again, drizzle in more oil to thicken. Add some water more juice if it turns to thick, add soy sauce until it turns light blond..finish up with a table spoon of sugar taste, add more juice, paste, etc to taste.
I'll sometimes add a touch of ginger juice if really needs it.
If you want sugar...grate a carrot and use that in the mix.